# Help Solving Equation Involving A Rational Exponential

Tags:
1. Mar 1, 2016

### Captain1024

1. The problem statement, all variables and given/known data
Solve $y=\mathrm{exp}(\frac{-x\pi}{\sqrt{1-x^2}})$ for x when y = 0.1

2. Relevant equations
$\mathrm{ln}(e^x)=x$

3. The attempt at a solution
$\mathrm{ln}(0.1)=\frac{-x\pi}{\sqrt{1-x^2}}$
$(\frac{-\mathrm{ln}(0.1)}{\pi})^2=\frac{x^2}{1-x^2}$

2. Mar 1, 2016

### ehild

It is all right so far. What is your problem? You got a simple equation for x2.

3. Mar 1, 2016

### SammyS

Staff Emeritus
One thing that will improve the looks of the right hand side. Recognize that −ln(0.1) is ln( (0.1)−1 )

Another thing you might try is to take the reciprocal of both sides of the equation.

4. Mar 1, 2016

### Captain1024

$x=\sqrt{\frac{1}{\frac{\pi ^2}{(\mathrm{ln}(10))^2}+1}}$

That's what I needed. Thank you.